Researchers have proposed a new formulation of the gravitational path integral using the concept of quantum reference frames (QRFs). These QRFs are gauge-covariant coordinate systems constructed from the available field content in gravity. The formulation is expressed in terms of relational (frame-dressed) observables and aims to provide a manifestly gauge-invariant path integral, free of ghosts and anomalies. In this approach, observables and their correlators are local to a specific reference frame, eliminating the need for gauge fixing.
A central feature of this proposal is its covariance under QRF changes, making it a perspective-neutral path integral. This means it encodes all internal QRF perspectives and the transformations between them. Although it eliminates the need for gauge fixing, the formulation is equivalent to Faddeev-Popov versions when the QRF is fixed, thus recovering some previous proposals. This framework leads to interesting qualitative predictions, such as local correlators and the time evolution of relational observables in one QRF perspective becoming fuzzy in another.
Furthermore, the theory predicts a new spectrum of relational vacua. A vacuum from one perspective may appear as a generally excited state from another, and these vacua include frame-dependent no-boundary and asymptotic ground states. Finally, the authors have constructed gauge-invariant yet frame-dependent effective actions by coupling sources exclusively to relational observables. This sets the stage for a relational definition of the renormalization process, a crucial step towards a consistent quantum theory of gravity.